Solve 1/3z^-5

$$\frac { 1 } { 3 z ^ { - 5 } }$$

Evaluate

$$\frac{z^{5}}{3}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\frac{1}{3z^{-5}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\frac{1}{3}\times \frac{1}{z^{-5}}$$

To raise a power to another power, multiply the exponents.

$$\frac{1}{3}z^{-5\left(-1\right)}$$

Multiply -5 times -1.

$$\frac{1}{3}z^{5}$$

Differentiate w.r.t. z

$$\frac{5z^{4}}{3}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(3z^{-5}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}z}(3z^{-5})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\left(3z^{-5}\right)^{-2}\left(-5\right)\times 3z^{-5-1}$$

Simplify.

$$15z^{-6}\times \left(3z^{-5}\right)^{-2}$$